Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
 
#define REP(i, s, n) for(int i = s; i < n; ++i)
#define rep(i, n)		 REP(i, 0, n)
#define SORT(c)			 sort((c).begin(), (c).end())
#define IINF					INT_MAX
#define LLINF					LLONG_MAX
#define DEBUG					false
 
typedef long long				ll;
typedef pair <int, int> ii;

int main() {
	
	int n;
	cin >> n;
	
	vector<int>a(n);
	rep(i, n) cin >> a[i];
	SORT(a);
	
	double ans = 0;
	
	for(int i  = n - 1; i > 0 ; i--){//C, D
		int bunnbo = a[i] - a[i - 1];
		int bunnsi;
		if(i == n - 1) bunnsi = a[n - 3] + a[n - 4];
		else if (i == n - 2) bunnsi = a[n - 1] + a[n - 4];
		else bunnsi = a[n - 1] + a[n - 2];
		ans = max(ans, (double)(1.0 * bunnsi / bunnbo ));
	}
	
	printf("%.6lf\n", ans);
	
	
	return 0;
}